Student epistemic framings for a conceptual physics test question

Tyler D. Scott1, Catherine McGough2, Lisa Benson2

1Northwestern College, 2Clemson University

IntroductionEpistmemic beliefs are an important facet of student development and success in introductory physics[1, 2]. Epistemic flexibility in problem solving is a hallmark of the development of expertise [3]. But aresophisticated and flexible epistemic beliefs being developed through assessments?

As any professor who has been asked “Will this be on the test?” knows, tests are the primary focus ofmany students. Though physics educators might try to develop mature epistemic beliefs in their students,many students only see value in what will help them succeed on assessments [4].

Therefore, this study seeks to better understand how students make sense of physics exams and problems.The work is guided by two research questions:

Q1. How do physics students’ framings of exams affect their responses to exam questions?Q2. What epistemic resources do students use when attempting to solve a question without a nu-

meric or symbolic answer?

Here the term “framing” is defined by as the answer to the question, “what kind of activity is going onhere?” [5].

Data Sources• Student answers on a test question

• Post-test reflection essays

Students were asked about what methods they used to try to solve the problem and, if they conceptu-ally knew the answer, what were their reasons for questioning their conceptual understanding.

• Population: 13 students in a calculus-based, introductory physics course

The Test Question

The angle that a swinging, simple pendulum makes with the vertical obeys the equationΘ(t) = (0.150rad) cos[(2.85rad/s)t + 1.66]

A.) What is the length of the pendulum?B.) What is the mass of the swinging bob at the end of the pendulum?

Unfortunately, the students struggled with the fact that no numeric or symbolic solution existed to part B.Though most would have probably gotten the question correct in the multiple choice format, only threedid in this scenario.

“Although I did know that the period [of the pendulum] is independent of the mass. . . I figured thatsince it was a short answer question, there had to be a way to calculate mass. The fact that I assumedwe wouldn’t be given a question incapable of being solved, I didn’t give up on the problem until Ihad a numerical answer.”

— Jackie

Students’Test Framing

Students’ Epis-temic Resources

Students’ TestResponses

Assesmentof StudentLearning

Epistemic Resource FrameworkThe student reflections were analyzed using a set of preexisting codes while also allowing for emergentcodes. The preexisting codes corresponded to four epistemic resources [5].

Calculation: “Algorithmically following a set of established computational steps should lead to atrustable result.”

Physical Mapping: “A mathematical symbolic representation faithfully characterizes some feature ofthe physical or geometric system it is intended to represent.”

Invoking Authority: “Information that comes from an authoritative source can be trusted.”

Math Consistency: “Mathematics and mathematical manipulations have a regularity and reliabilityand are consistent across different situations.”

“I recall looking through my theorem sheet, looking for equations for pendulums that involved mass.When I couldn’t find any equations, I began trying to manipulate equations in efforts to re-write themin terms of mass.”

— Helen

Results

Test Framing

The following test framing codes emerged:

• Test questions have a numeric or symbolic solution.

• Test questions always have one right answer.

• Short answer test questions always have enough information to find a numerical solution.

• Test questions use equations from the equation sheet.

Resource Use

• Every student invoked at least one of two types of authority.

1. Equation sheet2. Class related authority

• Invoking authority was usually followed by a calculation.

• A math consistency resource was rarely used and was difficult to separate from a calculation.

• Physical mapping was rarely used.

My initial plan was to use my equation sheet [to] find an equation linking mass and length.

— Ulysses

My first thought went back to the lab that we did at the beginning of the semester with the pendulum.During that experiment, we were told the mass was not relevant and that was my first clue that theanswer to this problem might not be numerical.

— Julia

Conclusions and Future WorkMost students failed to successfully answer the problem because their framings of a physics test failed toaccount for a short answer question without a numeric or symbolic answer. They expected that any otheranswer would be explicitly suggested by multiple-choice options or legitimized by the instructor.

The data also showed that students primarily focused on invoking authority and calculations as their epis-temic resources. This is not surprising as student expectations for exams are that solutions are normallynumeric or symbolic.

Originally, I wrote. . . “the motion of a simple pendulum is independent of mass.” However, I changedmy answer because “you can’t” is never an acceptable answer on a test. . . I wasn’t confident enoughto say, “there is no way to do this” because usually if that is an acceptable answer, that is explicitlystated either in the directions or by the professor.

— Hannah

We see potential for future work in the following areas:

• deliberate focus on student framings of physics tests and other formal and high-stakes assessments

• comparison of student reflections on problem solving and conceptual understanding to quantitativemeasures of conceptual understanding

• connection of the epistemic resource framework with metacognition and self-regulation frameworks

AcknowledgmentsThe authors would like to thank the physics students who were kind enough to write reflections abouttheir experiences on this problem. Despite their unhappiness about being “tricked,” they wrote interestingcomments that gave valuable insight into their thought patterns.

Tyler Scott would also like to thank the American Association of Physics teachers for the support theyprovided to assist him in attending the AAPT meeting and Physics Education Research Conference.

References[1] D. Hammer, “Epistemological Beliefs in Introductory Physics,” Cognition and Instruction, vol. 12, no. 2, pp. 151–183, 1994.

[2] L. Lising and A. Elby, “The impact of epistemology on learning: A case study from introductory physics,” American Journal of Physics, vol. 73,no. 4, p. 372, 2005.

[3] T. J. Bing and E. F. Redish, “Epistemic complexity and the journeyman-expert transition,” Physical Review Special Topics - Physics EducationResearch, vol. 8, pp. 1–11, 2012.

[4] A. Elby, “Another reason that physics students learn by rote,” American Journal of Physics, vol. 67, no. 7, pp. S52–S57, 1999.

[5] T. J. Bing and E. F. Redish, “Analyzing Problem Solving Using Math in Physics: Epistemological Framing via Warrants,” Physical Review SpecialTopics - Physics Education Research, vol. 5, 2009.